ok, first I'm assuming you are talking about DesktopX and not DirectX which is a 3D programming API developed by Microsoft.
1) Right-click on the DX system tray icon and select Configure DesktopX, Select the DesktopX tab on the dialog that is displayed and make sure "Run DX on startup" is checked. This should solve the DX not running when you reboot problem.
2) I'm not sure if this is a problem, but I would think this is the behavior you would want
3) When you launch DX it may be loading the default theme, if you want it to use the same theme every time you reboot, right-click on the DX system tray icon and select "Load Theme". Once you've loaded the theme right-click the system tray icon again and select re-start DX (just to make sure it loads the correct theme).
4) To get rid of objects you don't want right-click on the object and select "Delete Object", if you are asked whether you want to delete related objects click 'Yes'. You should be able to do this for all of the objects you don't want. When you say it's not showing the objects for the theme you just installed, have you installed the theme yet? Just downloading it won't install it. You have to find the downloaded file and double-click it to install it and them you may need to Load it as I explained above.
I believe this is what will happen, but as I said just downloading the theme will NOT install it. You have to double-click on the downloaded file to install it. I believe it will auto-load when you install it, if not just follow the above directions to load it.
I have CursorXP Pro and have for ages so I'm not sure whether the free version has reminders but if it does I'm pretty sure you'll continue to get them until you upgrade.
No, LogonStudio is a free program. If it's asking you to register you might want to send a message to Stardock tech support and find out if there is a fix for this.
HTH!